Melting glaciers in Antarctica and Greenland may push up global sea levels more than 3 feet by the end of this century, according to a scientific poll of experts that brings a degree of clarity to a murky and controversial slice of climate science.

Such a rise in the seas would displace millions of people from low-lying countries such as Bangladesh, swamp atolls in the Pacific Ocean, cause dikes in Holland to fail, and cost coastal mega-cities from New York to Tokyo billions of dollars for construction of sea walls and other infrastructure to combat the tides.

"The consequences are horrible," Jonathan Bamber, a glaciologist at the University of Bristol and a co-author of the study published Jan. 6 in the journal Nature Climate Change, told NBC News.

Estimating how much sea levels will rise from ice sheet melting is one of the more challenging aspects of climate science. Some evidence suggests recent accelerated melting is related to changes in ocean and atmospheric temperature, though natural variability may play an important role.

In addition, glaciers respond to external forces such as warmer temperatures in different ways, even when they are located right next to each other. As a result, there is tremendous uncertainty in the scientific community over how the melting will affect sea levels over the next century.

Bamber and colleague Willy Aspinall attempted to find clarity in the chaos using a scientific polling technique common in fields such as predicting earthquakes and volcanic eruptions, but until now not applied to climate science.

The pair sent 26 of the world's leading glaciologists a series of questions about the behavior of the Antarctic and Greenland ice sheets. About half replied to the survey in 2010. The respondents were polled again in 2012 to assess the robustness of their answers.

Bamber said this type of approach is "a lot more than an opinion poll." The experts were handpicked to get a representative perspective of world leaders from the ice sheet modeling and observational fields. "We analyzed the results in a very systematic, rigorous, and statistically robust way," he added.

The median estimate from the experts is that the melting ice sheets will contribute 1 foot (29 centimeters) to sea level rise by the year 2100 with a 5 percent chance their contribution could exceed 2.8 feet (84 centimeters). When the effect of thermal expansion (water expands as it warms) is taken into account, the high-end estimate is more than 3 feet (1 meter).

The estimates are higher than the controversial figures in the 2007 report from the Intergovernmental Panel on Climate Change (IPCC) of up to 23 inches (59 centimeters) and higher than the unpublished estimates being prepared for the next IPCC report, said Bamber, who is a review editor for that document and has seen the estimates.

"The numbers we are getting out of our elicitation reflect the fact that the world leaders in this field are now cognizant of the fact that the ice sheets are quite responsive and, in particular, there is a potential for them to make a really quite dramatic contribution," Bamber said.

The greatest drama would be a more than 3-foot rise in sea levels from the combined effect of melting ice and thermal expansion, which the study indicates has a 1 in 20 chance of occurring.

How much of this drama can be attributed to human burning of fossil fuels, the study indicates, remains murky. “There is really no consensus amongst the experts we approached,” Bamber said. “That’s something that we in the scientific community need to address as a matter of urgency.”

John Roach is a contributing writer for NBC News Digital. To learn more about him, check out his website.